I believe it uses the chain rule, anyway. My professor told me in class the other day that the chain rule can be used so I would prefer if there was an answer utilizing the rule, but really, anything will do. These webwork problems kill me! TIA!
If ,
Calculate .
help!
I get all of that and I get that dy/dx = dy/du * du/dx and I have what you have above. I just cannot figure out how to relate the 3x^2 to x and what to do to differentiate at x. I'm trying to use all of the classic formulas of the chain rule but I have found myself quite baffled! I'm not fishing for an answer here, but maybe there's something I'm missing?
ok, so the reason you are having trouble with this is that you do not have a good grasp of composite functions. making composite function and multiplying functions are two totally different things! replacing x with a function is not the same as multiplying by the function.
if you have
then NOT
now try to work from that idea. you want to somehow write the function in terms of , and then replace the with . that is all
Okay. I think I understand now. Here's what I did now:
I rewrote the function of (7/6)x^3 as 3x^2 * (7/18)x, since I'm trying to rewrite the derivative in terms of 3x^2 so I can replace it with just x. I did that and was left with x * (7/18)x, multiplied it out to get (7/18)x^2.
But the answer is still wrong. I thought I had a pretty good grasp on this stuff, but apparently I was wrong! Am I still missing something?
that is wrong. you have an x left over. the only variable you want in your function is 3x^2, you want no x's beside it or anything. it must only be 3x^2 times some constant. try once more (plus, you should have realized that if you plug in 3x^2 into (7/18)x^2 you do not get (7/6)x^3 as you should)
I like this guy's method, watch and learn
YouTube - 1991 AHSME #21 - Functions